Duplicating a mesh with shape keys and rig distorts mesh
this is one way i found to solve your problem.

FIRST: put the 3d cursor where the copy of the mesh should go. (seting cursor to center then scaling -1 on X then resetting scale also works)

SECOND: duplicate the original mesh and move it to the 3d cursor.

THIRD: replace all the .L s with  .R s (or to the corresponding bone names)

this should let you mirror your shape keyed mesh fairly easily and should also combine (ctrl+j) without deleting or dirupting up your shape keys